Referring to FIG. 1, a conventional wheel connecting device can be installed at a bottom of a chair (not shown), and is suitable for mounting of a wheel 10 thereon. The conventional wheel connecting device includes a mounting seat 11, a shaft 12, and two retaining members 13. The mounting seat 11 includes an accommodating space 110 that is defined by a top wall 111 and a surrounding wall 112. The surrounding wall 112 extends downward from a periphery of the top wall 111, and has an inner surrounding surface 113 that surrounds the accommodating space 110. The shaft 12 has an upper segment 121 that is inserted into the accommodating space 110, and a lower segment 122 that is disposed under and connected to the upper segment 121, and that is adapted for mounting of the wheel 10. The upper segment 121 has an outer surface 123 formed with two spaced-apart surrounding grooves 124. Each of the retaining members 13 is disposed in a respective one of the surrounding grooves 124, and circles around the upper segment 121 of the shaft 12 in order to allow the shaft 12 to rotationally interact with the mounting seat 11.
However, there exists a considerable gap between the upper segment 121 and the inner surrounding surface 113, and given that the rotation of the shaft 12 can cause unintentional shaking, there is a tendency for the shaft 12 to collide with the surrounding wall 112 and make noises. Additionally, the mounting seat 11 also has to withstand the weight from the chair (and its user) as well as lateral forces from turning and moving, which renders the mounting seat 11 more likely to collide with the shaft 12.